The searchbox is not the form field component. It has not validation feature. If you would like to validate the input value of searchbox, get the text box object of searchbox first and then call 'validatebox' method to create your validation rules.
$('#tag').searchbox({
prompt:'enter the search text',
searcher:.....
}).searchbox('textbox').validatebox({
required:true,
validType:'length[10,15]'
});